We are now ready to show the results for our production cross section calculations.
In addition to the current LHC energy of \(\sqrt{s}=13\)  TeV, we have examined various center-of-mass energies
for the future hadron collider projects, such as \(\sqrt{s}=27\)  TeV, 33 TeV, 87 TeV and 100 TeV.
We first show in Fig. REF  the dilepton production cross section as a function of \(M_{Z^\prime }\) 
for three different \(x_H\)  values and various \(\sqrt{s}\)  values.
Since the cross section is proportional to \({g_X}^2\)  in the narrow width approximation,
we have shown the cross section normalized by \({g_X}^2\) .
Comparing the results shown in the top-left panel with the final ATLAS results on the \(Z^\prime \)  boson resonance search
at the LHC Run-2 [1]}, we can read off the upper bound on \(g_X\)  as a function of \(M_{Z^\prime }\) .
For example, \(g_X \lesssim 0.1\)  for \(M_{Z^\prime }=4\)  TeV and \(x_H \sim -1\) .
See [2]} for details.
In Fig. REF , the left column shows the resultant \(Zh\)  production cross section
as a function of \(M_{Z^\prime }\)  for the three \(x_H\)  values and various \(\sqrt{s}\)  values,
while the resultant \(Zh\)  production cross section as a function of \(x_H\) 
for \(M_{Z^\prime }=4\)  TeV is shown in right column.
In Fig. REF , we have also shown the dilepton cross section results for comparison.
